//                                MFEM Example 2
//
// Compile with: make ex2
//
// Sample runs:  ex2 -m ../data/beam-tri.mesh
//               ex2 -m ../data/beam-quad.mesh
//               ex2 -m ../data/beam-tet.mesh
//               ex2 -m ../data/beam-hex.mesh
//               ex2 -m ../data/beam-wedge.mesh
//               ex2 -m ../data/beam-quad.mesh -o 3 -sc
//               ex2 -m ../data/beam-quad-nurbs.mesh
//               ex2 -m ../data/beam-hex-nurbs.mesh
//
// Description:  This example code solves a simple linear elasticity problem
//               describing a multi-material cantilever beam.
//
//               Specifically, we approximate the weak form of -div(sigma(u))=0
//               where sigma(u)=lambda*div(u)*I+mu*(grad*u+u*grad) is the stress
//               tensor corresponding to displacement field u, and lambda and mu
//               are the material Lame constants. The boundary conditions are
//               u=0 on the fixed part of the boundary with attribute 1, and
//               sigma(u).n=f on the remainder with f being a constant pull down
//               vector on boundary elements with attribute 2, and zero
//               otherwise. The geometry of the domain is assumed to be as
//               follows:
//
//                                 +----------+----------+
//                    boundary --->| material | material |<--- boundary
//                    attribute 1  |    1     |    2     |     attribute 2
//                    (fixed)      +----------+----------+     (pull down)
//
//               The example demonstrates the use of high-order and NURBS vector
//               finite element spaces with the linear elasticity bilinear form,
//               meshes with curved elements, and the definition of piece-wise
//               constant and vector coefficient objects. Static condensation is
//               also illustrated.
//
//               We recommend viewing Example 1 before viewing this example.

#include "mfem.hpp"
#include <fstream>
#include <iostream>

using namespace std;
using namespace mfem;

int main(int argc, char* argv[])
{
    // 1. Parse command-line options.
    const char* mesh_file = "../data/rectPD2.mesh";
    int order = 1;
    bool static_cond = false;
    bool visualization = 1;

    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
        "Mesh file to use.");
    args.AddOption(&order, "-o", "--order",
        "Finite element order (polynomial degree).");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
        "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
        "--no-visualization",
        "Enable or disable GLVis visualization.");
    args.Parse();
    if (!args.Good())
    {
        args.PrintUsage(cout);
        return 1;
    }
    args.PrintOptions(cout);

    // 2. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral or hexahedral elements with the same code.
    Mesh* mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();

    if (mesh->attributes.Max() < 2 )
    {
        cerr << "\nInput mesh should have at least two materials and "
            << "two boundary attributes! (See schematic in ex2.cpp)\n"
            << endl;
        return 3;
    }

    // 3. Select the order of the finite element discretization space. For NURBS
    //    meshes, we increase the order by degree elevation.
    if (mesh->NURBSext)
    {
        mesh->DegreeElevate(order, order);
    }

    // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
    //    largest number that gives a final mesh with no more than 5,000
    //    elements.
    //{
    //    int ref_levels =
    //        (int)floor(log(5000. / mesh->GetNE()) / log(2.) / dim);
    //    for (int l = 0; l < ref_levels; l++)
    //    {
    //        mesh->UniformRefinement();
    //    }
    //}

    // 5. Define a finite element space on the mesh. Here we use vector finite
    //    elements, i.e. dim copies of a scalar finite element space. The vector
    //    dimension is specified by the last argument of the FiniteElementSpace
    //    constructor. For NURBS meshes, we use the (degree elevated) NURBS space
    //    associated with the mesh nodes.
    FiniteElementCollection* fec;
    FiniteElementSpace* fespace;
    if (mesh->NURBSext)
    {
        fec = NULL;
        fespace = mesh->GetNodes()->FESpace();
    }
    else
    {
        fec = new H1_FECollection(order, dim);
        fespace = new FiniteElementSpace(mesh, fec, dim);
    }
    cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
        << endl << "Assembling: " << flush;

    // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
    //    In this example, the boundary conditions are defined by marking only
    //    boundary attribute 1 from the mesh as essential and converting it to a
    //    list of true dofs.
    Array<int> ess_tdof_list, ess_bdr(mesh->bdr_attributes.Max());
    ess_bdr = 0;
    ess_bdr[1] = 1;
    fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);

    // 7. Set up the linear form b(.) which corresponds to the right-hand side of
    //    the FEM linear system. In this case, b_i equals the boundary integral
    //    of f*phi_i where f represents a "pull down" force on the Neumann part
    //    of the boundary and phi_i are the basis functions in the finite element
    //    fespace. The force is defined by the VectorArrayCoefficient object f,
    //    which is a vector of Coefficient objects. The fact that f is non-zero
    //    on boundary attribute 2 is indicated by the use of piece-wise constants
    //    coefficient for its last component.

    VectorArrayCoefficient g(dim);
    g.Set(0, new ConstantCoefficient(0.0));
    g.Set(2, new ConstantCoefficient(0.0)); 
    
    Vector pull_force(mesh->attributes.Max());
    pull_force = 0.0;
    pull_force(2) =  -0.01;
    pull_force(3) = 0.01;
    g.Set(1, new PWConstCoefficient(pull_force));


    LinearForm* b = new LinearForm(fespace);
    b->AddDomainIntegrator(new VectorDomainLFIntegrator(g));
    cout << "r.h.s. ... " << flush;
    b->Assemble();

    // 8. Define the solution vector x as a finite element grid function
    //    corresponding to fespace. Initialize x with initial guess of zero,
    //    which satisfies the boundary conditions.
    GridFunction x(fespace);
    x = 0.0;

    // 9. Set up the bilinear form a(.,.) on the finite element space
    //    corresponding to the linear elasticity integrator with piece-wise
    //    constants coefficient lambda and mu.
    Vector lambda(mesh->attributes.Max());
    lambda = 1.0;
    //lambda(0) = lambda(1);
    PWConstCoefficient lambda_func(lambda);
    Vector mu(mesh->attributes.Max());
    mu = 1.0;
    //mu(0) = mu(1);
    PWConstCoefficient mu_func(mu);

    BilinearForm* a = new BilinearForm(fespace);
    a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));

    // 10. Assemble the bilinear form and the corresponding linear system,
    //     applying any necessary transformations such as: eliminating boundary
    //     conditions, applying conforming constraints for non-conforming AMR,
    //     static condensation, etc.
    cout << "matrix ... " << flush;
    if (static_cond) { a->EnableStaticCondensation(); }
    a->Assemble();

    SparseMatrix A;
    Vector B, X;
    a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
    cout << "done." << endl;

    cout << "Size of linear system: " << A.Height() << endl;

#ifndef MFEM_USE_SUITESPARSE
    // 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
    //     solve the system Ax=b with PCG.
    GSSmoother M(A);
    PCG(A, M, B, X, 1, 500, 1e-5, 0.0);
#else
    // 11. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
    UMFPackSolver umf_solver;
    umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
    umf_solver.SetOperator(A);
    umf_solver.Mult(B, X);
#endif

    // 12. Recover the solution as a finite element grid function.
    a->RecoverFEMSolution(X, *b, x);

    // 13. For non-NURBS meshes, make the mesh curved based on the finite element
    //     space. This means that we define the mesh elements through a fespace
    //     based transformation of the reference element. This allows us to save
    //     the displaced mesh as a curved mesh when using high-order finite
    //     element displacement field. We assume that the initial mesh (read from
    //     the file) is not higher order curved mesh compared to the chosen FE
    //     space.
    if (!mesh->NURBSext)
    {
        mesh->SetNodalFESpace(fespace);
    }

    // 14. Save the displaced mesh and the inverted solution (which gives the
    //     backward displacements to the original grid). This output can be
    //     viewed later using GLVis: "glvis -m displaced.mesh -g sol.gf".
    {
        GridFunction* nodes = mesh->GetNodes();
        *nodes += x;
        x *= -1;
        ofstream mesh_ofs("displaced.mesh");
        mesh_ofs.precision(8);
        mesh->Print(mesh_ofs);
        ofstream sol_ofs("sol.gf");
        sol_ofs.precision(8);
        x.Save(sol_ofs);
    }

    // 15. Send the above data by socket to a GLVis server. Use the "n" and "b"
    //     keys in GLVis to visualize the displacements.
    if (visualization)
    {
        char vishost[] = "localhost";
        int  visport = 19916;
        socketstream sol_sock(vishost, visport);
        sol_sock.precision(8);
        sol_sock << "solution\n" << *mesh << x << flush;
    }

    // 16. Free the used memory.
    delete a;
    delete b;
    if (fec)
    {
        delete fespace;
        delete fec;
    }
    delete mesh;

    return 0;
}
